The period where a male experiences a flush/readjustment of hormones. Obviously they do not bleed, but he does experince IMSIrritable Male Syndrome.
Similar to PMS. They can gain weight, be highly moody, and have an increase or decrease in sexual drive.

"Why is Jimmy so moody lately?"

"He always gets like this around the first two weeks of the month. I'm pretty sure it's his male-period."